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Design of ultra dense passive optical network to support high number of end users

Kebede Tesema Atra

To cite this version:

Kebede Tesema Atra. Design of ultra dense passive optical network to support high number of end users. Optics / Photonic. Institut Polytechnique de Paris, 2021. English. �NNT : 2021IPPAT010�.

�tel-03306228�

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Design of Ultra Dense Passive Optical Network to Support High Number of End Users

Thèse de doctorat de l’Institut Polytechnique de Paris préparée à Télécom Paris

Ecole doctorale de l’Institut Polytechnique de Paris, n°626 (ED IP Paris) Spécialité de doctorat: Électronique et optoélectronique

Thèse présentée et soutenue à Ville de soutenance, le 06/05/2021, par

K

EBEDE

T

ESEMA

ATRA

Composition du Jury : Delphine MARRIS-MORINI

Professeur, Université Paris-Saclay (– C2N) Président Hélène CARRERE

Maître de conférences, INSA Toulouse Rapporteur

Josep PRAT

Professeur, Universitat Politecnica De Catalunya Rapporteur Nikos PLEROS

Maître de conférences, Aristotle University of Thessaloniki Examinateur Didier ERASME

Professeur, Télécom Paris Directeur de thèse

Cédric WARE

Maître de conférences, Télécom Paris Co-Directeur de thèse

Giancarlo CERULO

Ingénieur de recherche, III-V Lab Encadrant industriel

Fabienne SALIOU

Ingénieur de recherche, Orange Labs Invité

NNT : 2021IPPAT010

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Design of Ultra Dense Passive Optical Network

to Support High Number of End Users

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In memory of my sister Bethlehem Tesema (Asnakech)

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Résumé

Les nouveaux réseaux cellulaires de cinquième génération (5G) adoptent une architecture de réseau centralisée, tout en utilisant des technologies à ondes millimétriques pour la transmission sans fil. Une telle architecture nécessite une large bande passante optique ainsi que l'installation d'un grand nombre de transmetteurs-récepteurs optiques. Afin de rendre la prochaine génération de réseaux résidentiels et mobiles abordables pour l'utilisateur final, il est essentiel de transmettre le trafic des utilisateurs sur une liaison en fibre optique partagée de manière rentable. Pour cette raison, des réseaux optiques passifs (PONs), avec des configurations point-multipoint et le multiplexage en longueur d'onde (WDM), sont adoptés par la plupart des opérateurs de réseau d'accès, comme une solution de transport rentable. En outre, il est nécessaire de minimiser la consommation d'énergie par bit et de réduire le coût du transmetteur-récepteur, en fournissant des composants optiques à faible coût et à haut-débit qui peuvent fonctionner à différentes longueurs d'onde dans un système WDM.

Dans ce programme de recherche, nous avons étudié des modulateurs à électro-absorption réfléchissants (REAM) intégrés, de manière monolithique, avec des amplificateurs optiques à semi-conducteurs (SOA) pour réaliser des transmetteurs à faible coût et à haut-débit, pour applications dans les nouvelles générations des réseaux d'accès. Le principal avantage technique d'un EAM-SOA réfléchissant (REAM-SOA) est qu'il peut être utilisé pour réaliser des transmetteurs, indépendants de la longueur d'onde (achromatiques), sur une large gamme de spectre, avec des exigences de contrôle minimales, directement compatibles avec la réallocation des canaux de transmission. Ces caractéristiques permettent de réduire le niveau de planification du réseau (assignation de la longueur d'onde) requise par les opérateurs et ont, donc, un impact significatif sur la réduction du coût global du système.

Dans la première partie de cette thèse, nous présentons la conception des composants, en discutant leurs propriétés physiques de base : le système de matériaux utilisés, l'ingénierie de la structure de bande des régions actives MQW et les guides d'ondes optiques SI-BH. La technologie de fabrication est également décrite, en introduisant les étapes clés du procédé PIC-SIBH. Nous étudions des composants basés sur différentes configurations, pour des modulateurs de longueurs différentes (80, 100 et 150 micromètres). Nous analysons l’optimisation des EAM, en étudiant les caractéristiques de base, comme la bande passante électro-optique (E/O), l’efficacité de modulation et les effets de ‘chirp’. Dans la deuxième partie, nous discutons de la caractérisation des propriétés statiques et dynamiques de nos composants. Dans la troisième partie de cette thèse, nous montrons les performances de nos composants pour des transmissions numériques et analogiques. Dans le domaine numérique, nous avons obtenu une transmission indépendante de la longueur d’onde, jusqu’à 25 Gb/s en utilisant le format de modulation ‘non-return-to-zero (NRZ)’.

Avec des EAM de 100 µm, nous avons également démontré une transmission jusqu’à 50 Gb/s.

Dans le domaine numérique, nous avons démontré une transmission radio sur fibre jusqu’à 3 km, à 10 Gb/s, en accord avec les exigences du fronthaul 5G.

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Summary

Emerging cellular networks such as the fifth generation (5G) adopt centralized network architecture while using millimeter wave technologies for wireless transmission. Such an architecture requires large optical bandwidth as well as installing a large number of optical transceivers. In order to make the next generation of residential and mobile networks affordable to the end user, it is crucial to transmit the user traffic over a fiber optic link cost-effectively. For that reason, passive optical network (PON) based on wavelength division multiplexing (WDM) is adopted by most access network operators as a cost-effective transport solution. Furthermore, it is also necessary to minimize energy consumption per bit and reduce the transceiver cost by providing low-cost and high-speed optical components that can operate at different wavelengths in a WDM system.

In this thesis, we study reflective electroabsorption modulators (EAMs) monolithically integrated with semiconductor optical amplifiers (SOAs) to realize low-cost and high-speed transmitters for access network applications. The main technical advantage of a reflective EAM-SOA (REAM- SOA) is that it can be used as a wavelength-independent (colorless) transmitter over a wide range of spectrum with minimal control requirements, enabling interchangeable network equipment, which reduces the amount of network (wavelength) planning required by network operators and thus have a significant impact on reducing the overall system cost.

We start with the device design and provide an overview of the material system, device physics, technological aspects, mask layout and structure of the integrated circuit. We also use numerical simulations to study the optical as well as quantum characteristics of the devices. We study different device configurations based on three modulator lengths (80, 100, and 150 micrometers) in order to study different design tradeoffs such as electro-optic (E/O) bandwidth, modulation strength, and modulator-induced chirp. Then, we fully characterize our components in both static and dynamic modes. In digital domain, we achieve up to 16 km wavelength-independent transmission at 25 Gb/s using non-return-to-zero (NRZ) modulation format. With the 100-µm long EAM, we demonstrate transmissions up to 50 Gb/s NRZ. In analog domain, we demonstrate up to 3 km radio-over-fiber transmission at 10 Gb/s, satisfying the requirements of 5G fronthauling.

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Table of Contents

1. Introduction ... 1

1.1. Mobile Fronthauling Based on Passive Optical Network ... 3

1.2. Challenges Associated with Tunable Lasers ... 7

1.3. Proposed Network Architecture ... 10

1.4. State-of-the-Art Reflective Devices ... 12

1.5. Context of the PhD ... 13

2. Device Design and Technology ... 18

2.1. Material System ... 18

2.2. Vertical Device Design ... 23

2.3. Multiple Quantum Wells ... 25

2.3.1. Quantization of Energy ... 29

2.3.2. Density of States ... 32

2.3.3. Strained Quantum Wells ... 34

2.3.4. Effect of Strain on Electronic Band Profiles ... 36

2.4. Electronic Band Structures of Compressive Strained MQWs ... 37

2.5. Absorption Coefficient ... 38

2.5.1. Optical Confinement Factor ... 41

2.6. Polarization Sensitivity ... 43

2.7. Electroabsorption Effects ... 45

2.7.1. Quantum Confined Stark Effect ... 48

2.7.2. Carrier Sweepout Time and Saturation Characteristics ... 54

2.8. Amplifier Gain and Noise Figure ... 56

2.9. Fabrication and Epitaxial Growth Process Flow ... 60

2.10. Semi-Insulating Buried Heterostructure ... 63

2.11. Device Structure and Schematics ... 68

2.12. Optical Mask Layout ... 70

2.13. Summary and Discussion ... 72

3. Performance Analysis of Basic Building Blocks ... 74

3.1. Optimization of Spot-Size Converter ... 75

3.1.1. Simulation of Waveguide Structures ... 79

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3.1.2. Far-Field Measurement ... 84

3.2. Insertion Loss ... 86

3.2.1. Insertion Loss Estimation ... 86

3.2.2. Insertion Loss Spectrum ... 90

3.3. Amplifier Gain ... 92

3.3.1. Experimental Setup ... 92

3.3.2. Amplified Spontaneous Emission Spectrum ... 93

3.3.3. Current-Dependent Small-Signal Gain ... 96

3.3.4. Gain Spectrum ... 97

3.3.5. Gain Saturation ... 100

3.4. Amplifier Noise Figure ... 103

3.5. Modulator Static Extinction Ratio... 107

3.6. Dynamic Characteristics ... 113

3.6.1. Small-Signal Frequency Response ... 113

3.6.2. Modulator Induced Chirp ... 124

3.7. Summary and Discussion ... 137

4. System-Level Demonstrations ... 141

4.1. Digital Transmissions in the C-Band at 25 Gb/s ... 142

4.1.1. Experimental Setup ... 142

4.2. Digital Transmission in the O-Band at 25 Gb/s ... 150

4.3. Beyond 50G Digital Transmission in the O-Band ... 152

4.4. Analog Radio-over-Fiber Transmission ... 158

4.5. Summary and Discussion ... 164

5. Conclusion and Perspectives ... 166

5.1. Summary and Conclusion ... 166

5.2. Perspectives ... 168

List of Abbreviations ... 170

References ... 172

Curriculum Vitae ... 177

List of Publications ... 178

Acknowledgments... 179

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Chapter 1

1. Introduction

In a telecommunication system, the access network is the one that connects end users to the rest of the network, namely metro and core networks. Depending on the type of service provided, the user can be reached directly using a fiber optic cable (e.g., in fiber-to-the-home, FTTH) or via a wireless link (e.g., mobile communication systems). In the latter case, the user equipment (UE) connects to the radio unit (RU) at the cell site, which then relays the radio information to the digital unit (DU) for baseband processing, using radio-over-fiber (RoF) technology. The fiber link between the DU and the RU is known as the fronthaul network [1]−[3]. Most of the discussions in this chapter apply to both residential as well as mobile networks, but we focus on mobile fronthauling that applies to emerging cellular technologies such as 5G and beyond.

One of the advantages of RoF transmission is that the optical link is transparent to the type of radio signal being transmitted. The modulation scheme in the optical domain can be digital RoF (DRoF) or analog RoF (ARoF), where the former is simple but spectrally inefficient whereas the latter is spectrally efficient but prone to nonlinear effects, which can have a significant impact on the transmission error rate [3]. Concerning the protocol interfacing the DU and the RU, the most widely used type is the common public radio interface (CPRI) protocol, an industry specification that introduces functional splits in radio base stations into the radio equipment (RE), which is the RU in this discussion, and the radio equipment controller (REC), which is the DU [4].

Low loss of fiber optic cables provides a great flexibility in choosing a convenient location for installing the DU with respect to the RU. As such, the DU and the RU are separated by a few kilometers (e.g., in 3G and 4G) to a few tens of kilometers (e.g., in 5G and beyond), leading to a centralized radio access network (C-RAN) architecture [1][2].

The main advantage of a C-RAN architecture is that it allows sharing radio resources (e.g., sharing a pool of DUs by several RUs) and facilitates a centralized network management and processing capabilities. However, it also brings two important technical challenges in relation to: (i) the large

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amount of data traffic to be carried by the fronthaul network (the optical link), which requires expensive high-speed optical transceivers, and (ii) the latency requirement of the system in order to support time-critical services that are envisioned to be supported by 5G+ networks (e.g., autonomous vehicles, remote surgery, and collaborative robots) [1].

The first challenge arises from the bandwidth inefficiency of the CPRI protocol in CPRI-based DRoF transmissions, which is the most widely used type of interface in existing networks, whereas the second challenge is mainly due to the propagation delay inside a fiber optic cable when the DU and the RU are separated by several kilometers. Several alternative solutions are studied to achieve lower data rate interfaces without compromising the end-to-end delay [2], mainly focusing on functional splits, where some of the functionalities of the DU can be moved to the RU so that the required bandwidth in the optical link can be reduced by performing baseband processing partly at the RU, e.g., by introducing eCPRI [4] and Ethernet-based fronthauling [5], both of which are based on higher layer splitting (instead of the physical layer where CPRI’s splitting occurs).

Therefore, with these advancements, the access network is feeling the pressure not only of data traffic growth but also new requirements for mobile fronthauling such as ultra-low latency, high reliability, high availability, and supporting large number of connected users [6][7]. Most of these requirements arise from the evolution of cellular networks to a C-RAN architecture as it is the case for 5G networks, where the DU and the RU can now be separated by a fiber length of 10−20 kms [8], with the DU being located in the central office (CO) and the RU at the remote office (RO), also known as the cell site [1][2].

In the wireless part, millimeter wave (mmWave) technologies, for example in the 60-GHz range (V-band), are being widely studied, exploited, and licensed to take advantage of their inherently large spectral bandwidth [3]. Since the wireless transmission distance at such high frequencies is limited by high propagation loss (e.g., atmospheric and free space losses), network densification (i.e., installing a large number of small cells) is considered as a key deployment strategy in 5G in order to enhance the network capacity [5]. To cope with the challenges associated with mmWaves (e.g., link budget, complexity, and line-of-sight transmission), the small cells integrate beamforming (focusing wireless signals to a specific receiver) as well as beam steering (changing the direction of the radiation pattern) capabilities for 360° coverage, together with massive multiple input multiple output (MIMO) antenna configurations to maximize the user data rate [9].

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Nevertheless, network densification being a key deployment strategy in 5G and mmWaves that transmit only up to a few hundred meters taking over the wireless part, the number of high-speed optical transceivers required in the fronthaul network increases tremendously, raising a serious concern on component cost, energy consumption per bit, and equipment footprint. As a result, it is necessary to introduce cost-effective optical transceivers in order to make the next generation of cellular networks affordable to the end user. This work focuses on the realization of low-cost and high-speed optical transmitters with wavelength-independent (colorless) operational capabilities for access network applications.

To transmit radio signals between the RU and the DU using RoF technologies, most access network operators adopted passive optical network (PON) based on wavelength division multiplexing (WDM) as a low-cost transport solution. A key feature of a PON system is that the optical distribution network (ODN) is passive, meaning that only passive components constitute the ODN (the physical fiber and optical devices in the field) while active devices are installed only at the two end offices (the CO and the RO) [8].

1.1. Mobile Fronthauling Based on Passive Optical Network

In order to increase the capacity of the access network, the international telecommunication union (ITU) introduced WDM technology to the access network in its next-generation passive optical network 2 (NG-PON2) standard [8]. The standard defined four 100-GHz-spaced wavelength channels, each carrying a maximum of 10 Gb/s traffic so that the aggregate downlink capacity increases to 40 Gb/s (from the CO to the RO). In this configuration, a single optical line terminal (OLT) located in the CO (close to the DU) connects to multiple optical network units (ONUs) at the RO (close to the RU) either in a point-to-multipoint (PtMP) or a point-to-point (PtP) connectivity. The standard also defined another set of 8×50-GHz-spaced wavelength channels for overlay PtP connectivity [8]. In the upstream direction (ONU to OLT), each ONU transmits at a maximum data rate of 10 Gb/s (in the case of symmetric transmission). In the PtMP connectivity, the number of ONUs per OLT typically exceeds the number of available wavelength channels. As a result, a single wavelength channel is shared by multiple ONUs, and the standard recommends implementing a hybrid time and wavelength division multiplexing (TWDM) scheme for wavelength sharing [8]. For that reason, the standard is commonly referred to as TWDM-PON.

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Fig. 1.1 shows a schematic diagram of mobile fronthauling based on WDM-PON in a C-RAN architecture, where a pool of DUs in the CO connects to an array of OLT channel terminations (CTs) and is shared by several RUs in the RO [10]. A wavelength multiplexer (WM) such as an arrayed waveguide grating (AWG) combines the optical signals from the OLT transmitters and transmits them over a single fiber optic cable. At the receiver side, a second AWG demultiplexes the optical signals and send them to their respective ONUs. Instead of an AWG, a passive optical power splitter can also be used at the receiver side, but the ONUs in that case will require optical filters in front of them. In either case, after optical to electrical (O/E) conversion is performed by the ONU receiver, the information is relayed to the RU, to which the UE connects wirelessly.

Fig. 1.1. Schematic diagram of a WDM-PON system supporting 5G fronthauling in a C-RAN architecture. CT:

channel termination, SMF: single-mode fiber.

The actual implementation of the WDM-PON system (PtMP or PtP) to support 5G+ fronthauling depends on the system requirement regarding latency as well as the number of connected ONUs (number of available wavelength channels). In order to support time-critical services, a dedicated wavelength channel can be assigned to each ONU by using the PtP dense WDM (DWDM) approach defined in NG-PON2. The number of available wavelength channels can be further increased by implementing ultra-dense WDM (UDWDM) PON, which increases the channel count by reducing the spacing between neighboring channels, and it is a promising candidate for the fronthauling of emerging mobile networks [11].

ODN (Passive)

OLT CT1

OLT CT2

OLT CT3

OLT CTn

l1

l2

l3 ln

SMF DU Pool

Remote Office Central Office

RU RU

Power orl Splitter

Mobile Fronthaul Based on WDM-PON

UE

UE l1

l2

l3

ln Wavelength Multiplexer

ONU1

ONU2

ONU3

ONUn

10-20 km

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On the other hand, in order to further increase the capacity of the access network and thus meet the growing bandwidth demand because of emerging technologies such as 5G+ fronthauling and data center interconnects, current PON standards are pushing the channel rate to 50 Gb/s with a nominal line rate of 25 Gb/s as recommended by IEEE’s 50G EPON (Ethernet PON) [12] and 50 Gb/s as recommended by ITU’s 50G PON, also known as high-speed PON (HSP) [13]. That means, to achieve the 50G capacity, the former recommends multiplexing two 25-Gb/s wavelength channels whereas the latter recommends a single-wavelength capacity of 50 Gb/s.

Both standards use simple modulation formats such as non-return-to-zero (NRZ) on-off keying (OOK) so that low-cost transceivers can be used, but NRZ-OOK is not spectrally efficient.

Improving the spectral efficiency in the optical domain requires complex and expensive coherent detection, and, although it is being widely studied and getting cheaper, it is not yet the preferred option for high-speed access networks. In this thesis, we focus on NRZ modulation format, and we use PAM-4 (four-level pulse amplitude modulation) to show the capabilities of our components as a next step.

Apart from their differences in the nominal line rates (and protocols used for communication between OLT and ONU), the two standards (IEEE’s 50G EPON and ITU’s 50G PON) support coexistence of current PON technologies with legacy networks. As an example, Fig. 1.2 shows a simplified schematic diagram of a 50G PON system in coexistence with legacy PONs [13].

Fig. 1.2. Schematic diagram of a 50G PON system in coexistence with legacy PONs (after [13]). MPM: multi-PON module, Tx: Transmitter, Rx: Receiver.

Power Splitter SMF

Central Office ODN Remote Office

l1

l2

ln

Legacy PON ONU Legacy PON

ONU 50G PON

Tx Legacy PON Tx Multi-rate

Rx

Wavelength Multiplexer MPM

l1

l2

l3

50G PON ONU

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At the OLT side, the evolution from legacy to 50G PON can be realized using a multi-PON module (MPM) that incorporates a wavelength multiplexer together with the OLT transmitters or using an external coexistence (CEx) element [13]. The optical signals from different PON transmitters are multiplexed and transmitted over a single fiber. At the receiver side, a passive splitter (power or wavelength) splits the transmitted signals and sends them to a number of connected ONUs. Then, each ONU, equipped with appropriate type of receiver (e.g., a 50G capable receiver with an optical filter for 50G PON), receives the information on its operating wavelength.

Although the wavelength plan in the NG-PON2 standard is in the C-band (1.55 µm window), which is characterized by a relatively low fiber loss and high chromatic dispersion as shown in Fig. 1.3 (a), the transmission distance in the C-band is primarily limited by dispersion, which becomes more detrimental at bit rates >10 Gb/s. For that reason, both IEEE’s 50G EPON and ITU’s 50G PON standards defined their WDM wavelength plans in the O-band (1.3 µm window), which is characterized by a relatively high fiber loss and very low fiber dispersion.

Fig. 1.3 (b) shows the wavelength plans for downlink and uplink transmissions defined by ITU (top) and IEEE (bottom) for 50G applications [12][13]. In both cases, the upstream transmissions take place near the zero or negative dispersion regimes so that simple and cost-effective ONU transmitters can be used without experiencing significant performance degradation because of dispersion.

(a) (b)

Fig. 1.3. (a) Dispersion and loss spectra of standard single-mode fiber, (b) wavelength plans for 50G PON applications defined by ITU’s 50G PON (top) and IEEE’s 50G EPON (bottom). US: upstream, DS: downstream.

1300 1342

1270

US2 US1 DS

±10 ±10 ±2

ITU

IEEE

1300 1342

US1 DS1

±10 ±2 1358

DS0

±2 1320

US2

±2

Wavelength (nm)

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In addition to minimizing the cost of the transport network by implementing WDM-PON, it is also necessary to provide low-cost optical transceivers in order to minimize the overall system cost.

Moreover, the devices have to be realized using industrially compatible technologies so that they can be mass-produced for large-scale deployments.

Nevertheless, both standards (IEEE’s 50G EPON and ITU’s 50G PON) recommend using wavelength-tunable components on both sides of the network (at the CO and the RO) [12][13].

However, tunable devices require tight wavelength control, which in turn requires complex electronic circuitry for their operation and control at data rates >10 Gb/s. This complicates the device design and operation, making tunable devices still expensive solutions to be used in the access network with large-scale deployments. The two important challenges in using wavelength- tunable lasers in a PON system arise from: (i) the ONUs are required to operate in burst-mode transmission [8][13], which causes frequency drift during burst transmission [14]−[16], and (ii) the complexity associated with their tuning mechanisms. Both challenges are discussed in the following section using experimental results.

1.2. Challenges Associated with Tunable Lasers

Thermal Tuning of Lasers

For access network applications, cost-effective wavelength-tunable transmitters are mainly based on either directly modulated lasers (DMLs) or externally modulated lasers (EMLs). In the former case, the modulating electrical signal is directly applied to the laser whereas an external modulator such as an electroabsorption modulator (EAM) is integrated with the laser in the latter case. Among the two, DMLs are relatively simple, and they are widely used in short-reach applications, where the transmission distance is mainly limited by large chirp DMLs exhibit (a sudden change of laser wavelength, which causes pulse broadening and leads to intersymbol interference at the receiver side, and ultimately increases the transmission error rate) [17][18].

On the other hand, thermal tuning is the simplest wavelength tuning mechanism for such low-cost components, which can be achieved by integrating a heater on chip (for fast tuning) with a DML as illustrated in the lower part of Fig. 1.4 (a) [19]. In order to tune the laser, a DC current is applied to the heater for a duration of about 30 ms, and the emission wavelength of the laser is aligned to

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the edge of a tunable filter so that the transition from one wavelength to another, within the filter bandwidth (0.25 nm ≡ 30 GHz), can be captured by a sampling oscilloscope.

(a) (b)

Fig. 1.4. (a) SEM image of a DML with integrated heater, and shape of the heater driving signal applied to tune the laser by 2.4 nm (4×100 GHz), (b) signal captured by a sampling oscilloscope after the CW light passes through a tunable optical filter. λ1 = 1532 nm, λ2 = 1532.8 nm, λ3 = 1533.6 nm, λ4 = 1534.4 nm, Vscope ∝ 1/f.

Once the laser is tuned to the desired wavelength, its output power becomes constant (stable emission) so that a flat response is observed in the oscilloscope as shown in Fig. 1.4 (b). After a fast tuning is achieved by using the integrated heater, a thermoelectric controller (TEC) can slowly take over (the TEC has a lower response time than the integrated heater), keeping the DML’s operating temperature constant [19]. In this experiment, a constant DC current of 80 mA is applied to the laser whereas the heater current is varied between 0 mA and 220 mA (ΔT ≈ 24℃)—a higher heater current is required for a wider tuning range. Using this configuration, a tuning time of ~13 ms is achieved to tune the laser from 1532 nm to 1534.4 nm (2.4 nm range, equivalent to 4×100 GHz) as shown in Fig. 1.4 (b). This satisfies the recommended maximum tuning time of 25 ms for Class 2 applications in TWDM-PON for a 400-GHz spectral range (e.g., see Table 9-2 of [8]).

However, the heater alone consumes ~330 mW electrical power (220 mA × 1.5 V) to cover the four 100-GHz-spaced channels. Even this level of power consumption is achieved by applying several optimizations that improved the heater efficiency [19]. Therefore, in addition to the extra power consumption by the heater, thermal tuning complicates the design and driving circuitry of the device and thus increases the component cost.

Laser

Laser Current (80 mA, constant)

Heater

Scope l1-l4

Filter on

off 13 ms

l1 l4

2.4 nm

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9 Burst-Mode Operation of Lasers

When several ONUs share a single wavelength in the upstream direction of a TWDM-PON system, the output power of each ONU is required to be very low when it is not enabled (WNE) in order to minimize crosstalk on neighboring wavelength channels [8]. For example, the maximum WNE output power levels required for a 10-Gb/s symmetric transmission in the downstream and upstream directions are −63.7 dBm and −67.6 dBm, respectively [8]. Several proposed solutions are available in the literature to control the ONU output power. For example, Taguchi et al.

demonstrated a mechanism for controlling the burst-off output power of a wavelength-tunable laser by reverse biasing an integrated SOA that acts as an optical gate [20].

Burst-mode operation of a wavelength-tunable laser also causes a frequency (wavelength) drift because of thermal variation between burst on and off states [14]. One possible solution for stabilizing the emission wavelength of a laser operating in burst-mode is to use a counter-heating technique, where the chip is intentionally heated between bursts so that its average temperature remains constant [15][16]. Fig. 1.5 (a) shows a schematic diagram of the experimental setup used to measure the frequency drift on a tunable DML operating under burst-mode transmission with and without counter-heating.

(a) (b) (c)

Fig. 1.5. (a) Schematic diagram of experimental setup for measuring emission wavelength of a laser operating in burst- mode, (b) measured wavelength (frequency) without counter-heating, and (c) with counter-heating.

By aligning the continuous wave (CW) emission wavelength (frequency) of the laser with the edge of a tunable optical filter (30 GHz bandwidth), any frequency drift caused by burst-mode operation

Amplitude

Frequency (GHz) f0

f0-Df DML+

Heater Scope

Heater off

off on

Signal

on Heater

off on

Signal

off

10 ms

Amplitude → frequency Amplitude → frequency

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translates to an increase or a decrease in the output frequency. Without applying a counter-heating mechanism, the emission frequency of the laser continuously decreases (wavelength increases) until the burst ends as shown in Fig. 1.5 (b) with the worst-case performance occurring for a burst of 50% duty cycle [14][15]. When counter-heating is applied, the laser wavelength stabilizes within ~10 µs. Except for the transient frequency drift that occurs during this short period, the laser operates normally for the rest of burst transmission. However, this works well only in a system where there is sufficient gap between neighboring channels so that a certain transient frequency drift can be tolerated. Moreover, stabilizing the emission wavelength using counter- heating technique comes at the expense of extra power consumed by the heater and an additional circuitry for driving and controlling it, thereby increasing the component cost.

Another drawback of DMLs is that they exhibit large chirp (as high as +8.0) because they suffer from both adiabatic and transient chirp [18]. Although high-speed DMLs operating at bit rates ≥50 Gb/s have already been demonstrated in the O-band [21][22], the large chirp degrades their transmission performances in the C-band, limiting their usability to short-reach applications.

Therefore, in addition to the complexity associated with wavelength tuning mechanisms of lasers, both thermal and ONU power control mechanisms also increase the complexity of tunable components and increase their power consumptions, ultimately increasing the component cost, but colorless transmitters sidestep the problems associated with tunable transmitters.

In this thesis, we propose reflective EAMs (REAMs) monolithically integrated with semiconductor optical amplifiers (SOAs) as alternative transmitter solutions for low-cost and colorless access network applications, avoiding the need for wavelength tunability. Depending on the positions of the EAM and the SOA along the optical path, two photonic integrated circuit (PIC) configurations can be realized: REAM-SOA or its opposite RSOA-EAM, where the input light sees the EAM before the SOA in the former case and vice versa.

1.3. Proposed Network Architecture

Fig. 1.6 shows a schematic diagram of a WDM-PON system based on array of REAM-SOAs together with a comb-laser and a wavelength multiplexer, representing a multi-channel OLT transmitter for downlink transmission. The principle of operation is as follows: a series of CW optical lines generated by the comb-laser enters port-1 of an external optical circulator and leaves

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at port-2, which is connected to an AWG (wavelength multiplexer). The AWG demultiplexes the individual optical lines and sends them to their respective REAM-SOAs. The AWG can also be used to slice wavelengths when a broad source is used instead of a comb-laser [23][24].

Inside each REAM-SOA (see inset of Fig. 1.6), the input light is first amplified by the SOA and then modulated by the EAM in its forward path. The optical carrier is reflected when it hits the rear facet of the PIC (high reflection coated), further modulated by the EAM and reamplified by the SOA in its reverse path. After going through the double modulation and amplification processes, the optical signal is coupled to the output fiber, which is the same fiber used for input coupling. The same AWG that demultiplexed the optical tones now multiplexes the modulated optical signals readied for downlink transmission over a standard single-mode fiber (SMF). The external circulator enables bidirectional transmission over a single fiber. At the receiver side, a second AWG demultiplexes the transmitted signals and sends them to their respective ONUs.

Fig. 1.6. Schematic diagram of a WDM-PON based on array of REAM-SOAs for downlink transmission. Inset:

schematic of an REAM-SOA with an integrated spot-size converter.

A similar topology can be built for the uplink transmission by using the REAM-SOAs as ONU transmitters distributed across different sites as illustrated in Fig. 1.7. In this case, a remote seeding scenario can also be realized by placing the comb-laser in the central office close to the OLT and transmitting the CW optical carriers towards the ONUs to be reflected and modulated with uplink information. Moreover, since the OLT receivers exist as arrays in the central office, a pre-amplifier

REAM-SOA1

REAM-SOA2

REAM-SOA3

REAM-SOAk

ONU1 RX

ONU2 RX

ONU3 RX

ONUk RX l1

l2

l3

lk

AWG1 (Mux/Dmux)

l1

l2

l3

lk

Comb Generator Multi-channel

OLT Transmitter

SMF l1 lk

1

2 3

Central Office ODN Remote Office

AWG2 (Mux/Dmux)

AR

SOA SSC Light In

Light Out EAM

G G

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having wide bandwidth can be inserted in front of the AWG so that the receivers can be realized using low-cost PIN photodiodes with their sensitivities enhanced by the pre-amplifier.

Fig. 1.7. Schematic diagram of a WDM-PON system based on REAM-SOAs as ONU transmitters.

1.4. State-of-the-Art Reflective Devices

Most research activities that dealt with reflective devices in the past focused on realizing components that are compatible with the NG-PON2 standard (10 Gb/s NRZ operation and ≥20 km transmission in the C-band), mainly for the prospect of using the devices as colorless transmitters [25]−[27]. However, because of a relatively high chromatic dispersion in the C-band, there is a tradeoff between data rate and transmission distance. For example, Lawniczuk et al.

demonstrated a 40-Gb/s NRZ transmission using an REAM-SOA, but the transmission distance at this bit rate was limited to only 2 km at a bit error rate (BER) of 103 [28]. When operated at 10 Gb/s NRZ, the same device was able to transmit up to 25 km.

Similarly, 25 Gb/s NRZ transmissions have been demonstrated up to 20 km in [24][29]. However, both experimental demonstrations involved equalization techniques that increase the transmitter cost. Fig. 1.8 summarizes state-of-the-art REAM-SOAs showing a plot of data rate versus transmission distance. Several high-capacity transmissions based on arrays of REAM-SOAs have

OLT RX1

OLT RX2

OLT RX3

OLT RXk

REAM-SOA1

REAM-SOA2

REAM-SOA3

REAM-SOAk

l1

l2

l3

lk

l1

l2

l3

l4

Comb Generator OLT Receivers

SMF l1 lk

1

3 2

Central Office ODN Remote Office

ONU Transmitters (distributed)

amp

Uplink Transmission

AWG2 (Mux/Dmux) AWG1 (Mux/Dmux)

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been demonstrated, for example, with aggregate capacities of 113 Gb/s (10×11.3 Gb/s) [30], 400 Gb/s (40×10 Gb/s) [31], and 800 Gb/s (80×10 Gb/s) [23], all of which utilized 10G transmitters together with broad sources. Such high-density integration of reflective devices is appealing to realize multi-channel OLT transmitters for high-capacity WDM-PON systems and for bandwidth demanding short-reach data center interconnects. Therefore, increasing the achievable data rate per device is an important element to realize cost-effective transmitters for the next generation of high-speed access networks.

In this work, we demonstrate up to 16 km colorless transmission with a single-channel capacity of 25 Gb/s NRZ in the C-band [32] and up to 10 km unamplified transmission in the O-band [34].

We also show results operating the O-band device at 50 Gb/s using NRZ as well as PAM-4 modulation formats in a back-to-back (BtB) connectivity without equalization [34]. As a proof-of- concept, we also demonstrate a 1.2-m wireless V-band transmission followed by a 3-km SMF intermediate-frequency-over-fiber (IFoF) transmission at an aggregate bit rate of 10 Gb/s, which is obtained by multiplexing four 16-QAM signals (QAM: quadrature amplitude modulation) [35].

Fig. 1.8. State-of-the-art of REAM-SOAs based on NRZ modulation format ([35] is based on 16-QAM ARoF).

1.5. Context of the PhD

The objective of this PhD is to develop novel optoelectronic devices that can be used as low-cost transceivers in DWDM or even UDWDM PON systems, with a focus on 5G fronthauling, within

Current Work Literature

Equalized

[28]

[34]

[34] [32]

[24] [29]

[35]

[26] [25]

(IFoF) [33]

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the context of the 5GSTEP-FWD1 project. However, the devices can also find several application areas such as high-speed PONs and data centers. The goal is to realize those devices and demonstrate their operational capabilities in test beds representing practical systems. An important element in minimizing component cost is to realize the devices using robust and industrially compatible technologies so that they can be mass-produced for large-scale deployments. For that reason, our components leverage semi-insulating buried heterostructure (SI-BH) waveguide technology and butt-joint integration technique, both of which are compatible with indium phosphide (InP) semiconductor technology, which is mature and widely used technology for realizing active semiconductor devices.

Some of the key requirements of optical transceivers for PON applications are high power budget, high-speed operation, high device linearity, multi-wavelength or wavelength-independent (colorless) operation, less sensitivity to polarization state of light, low amplifier noise figure, low energy consumption, and minimal device footprint. The power budget depends on the average modulated output power of the transmitter (launch power), ODN losses (e.g., fiber attenuation, splitting, and connector losses), and receiver sensitivity. High-speed operation, on the other hand, depends on the types of modulators and receivers used in the system. For multi-wavelength operation, either tunable or colorless devices can be used but the former require complex device design and control circuitry as discussed above.

In this work, we propose a transmitter solution based on monolithically integrated reflective EAM- SOAs. The main technical advantage of an REAM-SOA is that it can be used as a colorless transmitter with minimal control requirements, enabling interchangeable network equipment, which minimizes the amount of network (wavelength) planning required by operators, reduces installation and inventory costs as well as operation and maintenance costs. Details of the device design and the structural differences between REAM-SOA and RSOA-EAM configurations are discussed in Chapter 2. Since the two PIC configurations have similar operating principles, the REAM-SOA configuration will be used for most of the discussions in this manuscript.

1 5GSTEP FWD (acronym for 5G System Technological Enhancements Provided by Fiber Wireless Deployments) is European Union’s Horizon2020 innovative training network (ITN) project under grant agreement number 722429.

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A reflective EAM-SOA can be used as an array (e.g., at the OLT side) or as a single transmitter element (e.g., at the ONU side), and some of its advantages are:

• Wavelength-independent (colorless) operation (avoids the need for tunability), which can have a significant impact on capital and operational expenses (CAPEX and OPEX).

• Large extinction ratio due to double absorption of light by the EAM section that occurs before and after reflection of the incident light.

• Low (or even negative) chirp, which is the primary advantages of EAMs over DMLs that allows the former to transmit relatively longer distances over a standard SMF in the C- band at bit rates beyond 10 Gb/s.

• The EAM section can be independently optimized in order to achieve very high electro- optic (E/O) bandwidth for high-speed applications without compromising the achievable extinction ratio.

• The possibility of using the REAM-SOA PIC for triple functionalities: as a transmitter, a PIN receiver, and for signal regeneration [36].

• The RSOA-EAM configuration can be used to perform bidirectional transmission using a single wavelength at the ONU side (wavelength reuse scheme), which can be achieved by splitting the downstream signal and feeding a portion of it to the RSOA-EAM (the other part goes to the ONU receiver), erasing the modulation by saturating the SOA section, and remodulating the CW optical carrier with uplink information by the EAM section [37][38].

• The devices are suitable for dense WDM integration as they require simpler driving circuitry compared to tunable devices, and they are less sensitive to thermal variations.

• The back facet of reflective devices can be used for running bonding wires, which avoids the need for complex bonding techniques such as flip-chip bonding.

• By monolithically integrating an SOA with the EAM, insertion loss of the PIC can be fully compensated, or even net device gain can be achieved through proper optimization.

The main drawback of an REAM-SOA is that it needs an external optical source. However, a multi-wavelength fixed source such as a comb-laser or a broad source can be shared by multiple

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ONUs, distributing the extra cost among different remote sites. Moreover, expensive optical equipment such as the comb-laser can be centralized in order to further reduce the system cost. As such, the CW optical carriers can be generated by a comb-laser located in the central office and sent to the remote offices, realizing a remote seeding scenario [23][24]. At the ONU side, the CW light from the CO is reflected, modulated by the EAM, amplified by the SOA, and transmitted back to the OLT at the CO, realizing a sourceless and colorless ONU.

Another drawback of an REAM-SOA is that both the EAM and the SOA sections can be sensitive to polarization state of the input light, which is the case for the devices studied in this thesis. Our components are more sensitive to transverse electric (TE) polarized light than transverse magnetic (TM) polarized light, which is due to the fact that compressive strained quantum-well layers that favor TE polarization are used in their active regions. But the polarization dependence can be minimized by proper choice of material compositions so that the amount of strain applied to the epitaxially grown thin layers is reduced or even compensated by using a combination of compressive and tensile strained quantum wells (e.g., see Section 2.3.3).

In this work, we analyze the building blocks separately as well as in integrated circuits in order to achieve optimal operating conditions and satisfy different requirements of PON systems. The three building blocks in our PICs are an EAM, an SOA and a spot-size converter (SSC). The requirement for the SSC is to provide minimal tapering, insertion and coupling losses. Moreover, it is also required to minimize optical feedback to the SOA gain section. On the EAM side, the key requirements are high dynamic extinction ratio, large E/O bandwidth for high-speed applications, and low driving voltage to minimize energy consumption as well as to be compatible with complementary metal-oxide-semiconductor (CMOS) technology and thus be able to integrate low- cost driver circuits with the PICs. Similarly, the main requirements for the SOA section are high amplifier gain (to improve the system power budget), low amplifier noise figure (NF), high saturation output power, and low-current operation.

The devices presented in this manuscript are based on a continuous mastering of device design, technological aspects, and fabrication processes for realizing high-performance optoelectronic devices at III-V Lab. The main contribution of this PhD is a complete performance analysis of the PICs at component level and using the devices at system levels, demonstrating their operational capabilities. Moreover, results obtained from optical simulation of SI-BH waveguides and

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quantum simulation of MQW structures can be used as inputs in the designs of the next generation of devices so as to improve their performances. The simulation results can also be used to relate experimental data to theory and validate the designs as well as any assumptions made during their theoretical treatments. Another contribution is the mask layout of the SSC section using Nazca Design2 based on parametric cell (PCell) design approach as part of an going activity to build component library.

The following chapters present the designs and performances of the devices, and the chapters are organized as follows: Chapter 2 presents the designs of the devices, technologies applied for their realization and relevant theories. We also show numerical simulation results regarding optical properties of our SI-BH waveguides obtained using FIMMWAVE3, and electrooptic properties of multiple quantum well (MQW) structures that make up the active regions of our components obtained using nextnano4. At the end of Chapter 2, we also present mask layouts of our PICs.

Chapter 3 presents a complete performance analysis of the devices using different PIC configurations, including a comparison of simulation and measurement results for the taper section. Chapter 4 presents system-level performances of our components based on transmission experiments using both digital and analog modulation formats as proofs-of-concepts, demonstrating the capabilities of our components under different operating conditions. At each stage, we indicate various design and operational tradeoffs and analyze their impacts on device performances. The fifth chapter presents concluding remarks and perspectives for future works.

2 Nazca is an open-source, Python-based design (scripting) tool for preparing mask layouts.

3 FIMMWAVE is a suit of 2D+Z waveguide mode solvers by PhotonDesign.

4 Nextnano is a quantum solver for simulating MQWs by solving Poisson-Schrödinger equations self-consistently.

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Chapter 2

2. Device Design and Technology

This chapter presents the design of our components and the technologies applied to realize them together with some relevant theories and simulation results to show different design aspects that need to be taken into consideration. The first section presents the material system used for realizing our photonic integrated circuits (PICs). Then, the vertical designs of the devices followed by different features of multiple quantum well (MQW) structures such as quantum confinement, strain and its effect on the electronic band structure of a semiconductor material are presented in Sections 2.2 to 2.4. Sections 2.5 to 2.7 present overview of absorption coefficient of an electroabsorption modulator (EAM), polarization sensitivity, and electroabsorption effects based on quantum confined Stark effect (QCSE). Section 2.8 highlights the main characteristics of a semiconductor optical amplifier (SOA). Section 2.9 presents the fabrication process flow highlighting different epitaxial growth steps. Different waveguide technologies are presented in Section 2.10, including semi-insulating buried heterostructure (SI-BH), which is the one used in our PICs. Section 2.11 presents the structures of our devices with their schematics illustrating the two PIC configurations studied in this thesis: reflective EAM-SOA (REAM-SOA) or its opposite RSOA-EAM. Finally, Section 2.12 presents the mask layout of our integrated circuits before concluding the chapter.

2.1. Material System

Semiconductors based on III-V materials (compounds consisting of elements from groups III and V of the periodic table) are commonly used for realizing optoelectronic devices for telecom applications. Among those materials, GaInAsP grown on InP substrate is a material of choice for long distance optical transmissions mainly for two reasons: (i) GaInAsP has a direct bandgap, (ii) it provides a wide range of bandgaps between 1.0 µm and 1.6 µm, which is the region where silica fiber has minimum dispersion (1.3 µm window, O-band) and loss (1.55 µm window, C-band) [39].

Our components are based on compressive strained GaInAsP/InP MQWs and are realized using SI-BH waveguide and butt-integration technologies.

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Fig. 2.1 (a) shows the bandgaps of binary constituents of GaInAsP as a function of lattice constant (distance between adjacent atoms) at 0K [39]. The binary compounds are GaAs, InAs, GaP, and InP. With the exception of GaP, which has an indirect bandgap as shown with dashed lines in Fig.

2.1 (a), the other three binaries have direct bandgaps (solid lines). However, all of them have a zincblende crystal structure formed by two interpenetrating face-centered-cubic lattices that are separated by a quarter of the lattice constant a as illustrated in Fig. 2.1 (b) [40].

(a) (b)

Fig. 2.1. (a) Bandgaps of constituent binaries of GaInAsP as a function of lattice constant (after [39]), (b) zincblende crystal structure (after [40]).

For direct bandgap materials, the valence band (VB) and the conduction band (CB) minima occur at the same point in an energy-wave vector (E-k) space at the center of the Brillouin zone (k = 0, also known as the Γ point) as illustrated in Fig. 2.2. (a), for example, for InP [41]. As a result, vertical electronic transitions (from VB to CB for absorption and CB to VB for emission) occur in direct bandgap materials whereas phonon assisted transition occurs in indirect bandgap materials as illustrated in Fig. 2.2 (b), reducing the transition efficiency in the latter case. For that reason, direct bandgap materials are widely exploited to realize optoelectronic devices for telecom applications such as lasers, modulators, detectors, and amplifiers.

The relationship between the bandgap (Eg) of a given material system and its atomic transition wavelength (λ) is given by: Eg = hc/λ ≈ 1.24/λmm [eV], where h is Planck’s constant, c is speed of light in vacuum, and λµm is the transition wavelength in micrometers. The bandgap of

C-Band O-Band

Ga0.47In0.53As GaP

GaAs InP

InAs

Metal Nonmetal x

GaInAsP

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GaxIn1−xAsyP1−y can be engineered by modifying compositions of the constituent binaries and thus devices operating in either of the two key telecom spectral ranges, the O-band (1260−1360 nm) or the C-band (1530−1565 nm), can be realized using the same material system (x and y are mole fractions of group III and V materials, respectively).

(a) (b)

Fig. 2.2. (a) Band structure of InP in the Brillouin zone centered at the Γ point (k = 0) (after [41]), (b) illustration of phonon assisted electronic transition in indirect bandgap materials.

High-performance optoelectronic devices can be realized by epitaxially growing thin layers of GaInAsP on an InP substrate. In order to grow high quality crystals on a relatively thick substrate, the lattice constant of the epitaxial layer can be matched to that of InP, which is achieved by properly controlling alloy compositions of the constituent binary materials. For ternary and quaternary alloys, their lattice constants can be calculated using Vegard’s law, which is based on a linear interpolation (weighted average) of lattice constants of their binaries. For example, the lattice constant a(x,y) of GaxIn1−xAsyP1−y can be obtained as [42][43]:

𝑎(𝑥,𝑦) = 𝑥𝑦𝑎(GaAs) + 𝑥(1 − 𝑦)𝑎(GaP) + (1 − 𝑥)𝑦𝑎(InAs) + (1 − 𝑥)(1 − 𝑦)𝑎(InP), (2.1) where, a(GaAs), a(GaP), a(InAs), and a(InP) are respective lattice constants of the binaries.

For GaInAsP lattice-matched to InP, a(x,y) of (2.1) equates to a(InP), providing a simple matching condition expressed in terms of the mole fractions as: x ≈ 0.47y [42]. The thick vertical line in Fig.

2.1 (a) represents the matching condition for GaInAsP, and its lowest point (open circle) is obtained for y = 1, which results in Ga0.7In0.53As. For practical applications, where the quantum

Eg

L L G D X

-14 -10 -6 -2 2 6

Eg

Band Structure of InP (Direct)

G6

G7 G8

G6

G7

G8

-12 -8 -4 0 4

Energy (eV)

Energy (eV)

Wave Vector (k)

Phonon Assisted Transition (Indirect) Phonon

Wave Vector (k) G

Eg

L X

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well thickness is several nanometers (up to ~20 nm, below critical thickness), a lattice mismatch of ~1% is acceptable, which results in strain (compressive or tensile) on the epitaxial layers [18][39]. Strain is exploited in tailoring different characteristics of optoelectronic devices (e.g., polarization sensitivity, modulation speed of EAMs, and threshold currents of SOAs and lasers).

Although linear interpolation using Vegard’s law works for calculating lattice constants of ternary and quaternary materials, it does not necessarily hold true for other parameters such as bandgap energy, lattice thermal conductivity, and effective masses [44][45]. In that case, a nonlinear factor called ‘bowing parameter’ is introduced for correction [44]−[46]. Its value is typically positive for III-V compounds, meaning that the actual bandgap of an alloy is less than the one that can be obtained by applying Vegard’s law [39], which is the reason why the lines connecting the binaries in Fig. 2.1 (a) are slightly bent towards the lower end of the y-axis. For a ternary material T of the form ABxC1−x, its nonlinear parameters that go beyond Vegard’s law (e.g., bandgap Eg) can be approximated to a quadratic function as [44][45]:

𝑇𝐴𝐵𝐶(𝑥) = 𝑥𝐵𝐴𝐵+ (1 − 𝑥)𝐵𝐴𝐶+ 𝑥(1 − 𝑥)𝐶𝐴𝐵𝐶, (2.2) where, TABC is the ternary material’s nonlinear parameter, BAB and BAC are the corresponding parameters of binaries AB and AC, and CABC is the bowing parameter.

Accordingly, nonlinear parameters of a quaternary alloy Q of the form AxB1−xCyD1−y can be obtained from the parameters of the constituent binaries and ternaries as [44][45]:

𝑄(𝑥, 𝑦) = 𝑥(1 − 𝑥)[𝑦𝑇𝐴𝐵𝐶(𝑥) + (1 − 𝑦)𝑇𝐴𝐵𝐷(𝑥)] + 𝑦(1 − 𝑦)[𝑥𝑇𝐴𝐶𝐷(𝑦) + (1 − 𝑥)𝑇𝐵𝐶𝐷(𝑦)]

𝑥(1 − 𝑥) + 𝑦(1 − 𝑦) . (2.3)

In most analytical systems, a constant bowing parameter is used, which can be extracted by fitting experimental data to functions. In numerical simulations, however, a more complex approach is employed (e.g., by using a bowing parameter that depends on alloy compositions). For example, up to thirteen parameters are used in nextnano5 for calculating the bandgap of a quaternary of the form AxB1−xCyD1−y [47]−[49].

Fig. 2.3 (a) illustrates the effect of bowing parameter on the bandgap of GaxIn1−xAsyP1−y, which also applies to any quaternary of a similar form. The borders are defined by the binary materials

5 Nextnano is a quantum solver software used for simulating electronic and optoelectronic devices, for example, to solve the Schrödinger-Poisson equations self-consistently.

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and the lines connecting them are the ternaries, with straight lines representing linear interpolation whereas the curved lines are when bowing parameter is included.

(a) (b)

Fig. 2.3. (a) Schematic illustration of bandgaps with and without bowing parameter for GaInAsP (after [47]) [straight lines: linear interpolation, curved lines: with bowing parameter), (b) composition diagram of GaInAsP [solid lines:

bandgap energies in eV, dashed lines: lattice constants in Å, hatched region: GaInAsP becomes indirect bandgap].

For analytical purposes, generalized interpolation formulas available in the literature can be used to estimate the bandgap as well as lattice constants of quaternaries, which typically are generated by fitting experimental data to functions. For example, for GaxIn1−xAsyP1−y, the bandgap at room temperature can be expressed in terms of alloy compositions x and y as [50]:

Eg(x, y) = 1.35 + 0.668x - 1.068y + 0.758x2 + 0.078y2- 0.069xy - 0.322x2y + 0.03xy2. (2.4) Similarly, its lattice constant is approximated as [50]:

𝑎(𝑥, 𝑦) = 5.8688−0.4176x + 0.1896y + 0.0125xy. (2.5) Fig. 2.3 (b) shows composition diagram of GaInAsP calculated using (2.4) and (2.5). The solid lines represent bandgaps in electronvolt (eV), and the dashed lines are lattice constants in angstrom (Å). The thick dashed line (red color) represents the lattice-matching condition for GaInAsP to an InP substrate, and the hatched region on the right-hand side of the figure is the region where GaInAsP becomes an indirect bandgap material (i.e., the composition of GaP dominates).

InAs GaAs

0 1

InAsyP1-y

GaxIn1-xP

GaAsyP1-y

GaxIn1-xAs

Linear interpolation With bowing parameter

x y

GaP InP

0 1

GaxIn1-xAsyP1-y

InAs GaxIn1-xAs

GaxIn1-xP

GaAsyP1-y

InAsyP1-y

GaAs

InP GaP

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